In terms of theoretical performance analysis, we prove that the DSSL algorithm converges to the stable matching allocation, and the regret has a logarithmic order with time. When comparing to existing approaches, DSSL achieves this under the more general restless Markovian model, and also has significantly better scaling with the system parameters. Specifically, under a common benchmark setting of equal rates among users (but still vary among channels), and \(K>M\) , which allows a theoretical comparison of learning efficiency between different algorithms, in [1]} and [2]} the regret scales as \(O(\frac{MK}{(\Delta _{\min })^2}\log (t))\)  ,in [3]} as \(O(\frac{M^3K}{(\Delta _{\min })^2}\log (t))\)  and in [4]} the regret scales as \(O(\frac{MK^2}{(\Delta _{\min })^2}\log (t))\) , where \(\Delta _{\min }\)  is the difference in rates between the \(M\) th and \((M+1)\) th best channels. In contrast, under DSSL, the regret scales as \(O((\frac{1}{(\Delta _{\min })^2}+MK)\log (t))\) . In addition, extensive numerical experiments were performed to demonstrate the efficiency of the proposed DSSL algorithm.
